Question

因式分解：9(x+y)^2+30(x+y)+25 已知A=3a^2-2a+5,B=8a^2-6a-8,A+B+C=1,求C 已知x+yx+y=5,x^2+y^2=9求xy

的值

Answer 1

9(x+y)^2+30(x+y)+25=[3(x+y)+5]²=(3x+3y+5)²

A+B+C=1,
则C=1-A-B=1-3a^2+2a-5-8a^2+6a+8=4-11a²+8a

x+y=5,
则(x+y)²=x²+2xy+y²=5²=25
因为x^2+y^2=9
所以2xy=25-19=6
所以xy=3

Answer 2

9(x+y)^2+30(x+y)+25
=[3(x+y)]^2+2×5×3(x+y)+5^2
=[3(x+y)+5]^2=(3x+3y+5)^2

A+B=11a^2-8a-3
C=1-(A+B)=4+8a-11a^2

x^2+y^2=(x+y)^2-2xy=9
x+y+xy=5
得：x+y=5-xy
(5-xy)^2-2xy=9
(xy)^2-10xy+25-2xy-9=0
(xy)^2-12xy+16=0
xy=(12±√80)/2=6±2√5

Answer 3

1、解：9(x+y)²+30(x+y)+25
＝[3(x+y)]²+30(x+y)+5²
＝[(3x+3y)+5]²
2、解：A=3a²-2a+5,B=8a²-6a-8,A+B+C=1
∵A+B+C=1
∴C=1-A-B
=3a²-2a+5-﹙8a²-6a-8﹚
=3a²-8a²-2a+6a+5+8
=-5a²+4a+13
3、x+yx+y=5,x²+y²=9
x²+y²+2xy-2xy=9
(x+y)²=9+2xy (1)
∵x+yx+y=5
x+y=5-xy (2)
将（2）代入（1）得：（5-xy）²=9+2xy
25-2xy+(xy)²-9-2xy=0
16-4xy+(xy)²=0
最后一个题好像有点题哦，你在看一下题